document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1121413>Question 1121413</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The ATM at a local convenience store allows customers to make withdrawals of $10, $20, $50, or $100. Let X denote a random variable that indicates the amount withdrawn by a customer. The probability distribution of X is<BR>\n" );
document.write( "P(10) = 0.2<BR>\n" );
document.write( "P(20) = 0.5<BR>\n" );
document.write( "P(50) = 0.2<BR>\n" );
document.write( "P(100) = 0.1<BR>\n" );
document.write( "(a) Draw the probability distribution of X.<BR>\n" );
document.write( "(b) What is the probability that a customer withdraws more than $20?<BR>\n" );
document.write( "(c) What is the expected amount of money withdrawn by a customer?<BR>\n" );
document.write( "(d) The expected value is not a possible value of the amount withdrawn. Interpret the expected value for a manager.<BR>\n" );
document.write( "(e) Find the variance and standard deviation of X. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #737310 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=737310\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Prob >$20 is 0.3<BR>\n" );
document.write( "E(X)=0.2*10+0.5*20+0.2*50+0.1*100=$32<BR>\n" );
document.write( "The expected value may be considered to be a weighted average, how much will be withdrawn on average. In other words, the expected value*the number of people withdrawing will be about what the total amount of money needed is.<BR>\n" );
document.write( "variance is $22^2*0.2+$12^2*0.5+$18^2*0.2+$88^2*0.1=$96.80+$72+$64.80+$774.40=$1008<BR>\n" );
document.write( "sd is sqrt (V)=$31.75 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );